Problem: In Takahashi's mind, there is always an integer sequence of length 2 \times 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9}) and an integer P.

Initially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.

When Takahashi eats symbols `+`, `-`, `>` and `<`, the sequence A and the integer P will change as follows:

* When he eats `+`, the value of A_P increases by 1;
* When he eats `-`, the value of A_P decreases by 1;
* When he eats `>`, the value of P increases by 1;
* When he eats `<`, the value of P decreases by 1.



Takahashi has a string S of length N. Each character in S is one of the symbols `+`, `-`, `>` and `<`. He chose a pair of integers (i, j) such that 1 \leq i \leq j \leq N and ate the symbols that are the i-th, (i+1)-th, ..., j-th characters in S, in this order. We heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last. How many such possible pairs (i, j) are there?

Constraints

* 1 \leq N \leq 250000
* |S| = N
* Each character in S is `+`, `-`, `>` or `<`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the answer.

Examples

Input

5
+>+<-


Output

3


Input

5
+>+-<


Output

5


Input

48
-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><<


Output

475

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
 
typedef unsigned long long ull;
const ull M=998244353;
const ull N=1000000007; 
const ull X=99431;
const ull Y=99487;
ull R;
ull L;
const int W=800;
 
 
ull ModPow(ull x, ull n, ull mod) {
        ull ret = 1;
        for (; n > 0; n /= 2, x = (x * x) % mod)
            if ((n & 1) == 1) ret = (ret * x) % mod;
        return ret;
    }
 
ull has=0,vec=1;
ull has2=0,vec2=1;
 
int n;
string s;
unordered_map<ull,int> B[550];
long long ans;
inline void calc(char c, ull &u,ull &p,ull &v,ull &q){
	if(c=='+'){u+=p;v+=q;}
	else if(c=='-'){u+=M-p;v+=N-q;}
	else if(c=='>'){p=(p*X)%M;q=(q*Y)%N;}
	else {p=(p*R)%M;q=(q*L)%N;}
	if(u>=M)u-=M;
	if(v>=N)v-=N;
}
int main(){
	R=ModPow(X,M-2,M);
	L=ModPow(Y,N-2,N);
	cin>>n>>s;
    //n=250000;
    //s=string(n,'+');
	for(int i=0;i<n;i++)calc(s[i],has,vec,has2,vec2);
	for(int i=0;i<n;i++){
		if(i%W==0)continue;
		ull h=0,x=1,hh=0,y=1;
		for(int j=i;j<n;j++){
			if(j%W==0)break;
			calc(s[j],h,x,hh,y);
			if(h==has&&hh==has2)ans++;
		}
		ull nh = (has+M-h)%M;
		nh = nh * ModPow(x,M-2,M)%M;
		ull nh2 = (has2+N-hh)%N;
		nh2 = nh2 * ModPow(y,N-2,N)%N;
		B[i/W+1][nh*N+nh2]++;
	}
	for(int i=0;i<n;i+=W){
		ull h=0,x=1,hh=0,y=1;
		for(int j=i;j<n;j++){
			calc(s[j],h,x,hh,y);
			if(h==has&&hh==has2)ans++;
			auto it = B[i/W].find(h*N+hh);
			if(it!=B[i/W].end())ans+=it->second;
		}
	}
	
	cout<<ans;
 
 
}